The present invention pertains generally to devices and methods for separating ions of relatively high mass to charge ratios (M1) from ions of relatively low mass to charge ratios (M2), when both are present in a multi-species plasma. In particular, the present invention pertains to devices incorporating plasma mass filter technology that relies on crossing an axially oriented magnetic field with an outwardly-directed and radially-oriented electric field. More particularly, but not exclusively, the present invention pertains to plasma mass filters that incorporate plasma mass filter technology with inputs of multi-species plasma densities above a predetermined collisional density for the plasma.
In a conventional plasma centrifuge, all of the ions in the plasma, both light and heavy ions, are in what is commonly called a potential well. In this condition, they are localized in a region where the potential energy of each ion is appreciably lower than it would be outside the region. Thus, such a potential well effectively forms a trap for the ions of a rotating plasma that tends to confine the ions. Furthermore, conventional plasma centrifuges operate in a collisional regime wherein the density of ions in the plasma causes them to collide with each other. For the operation of a plasma centrifuge, these collisions are necessary because they transfer energy between the ions in a manner that causes the heavier ions to accumulate near the periphery of the rotating plasma. At the same time, lighter ions are confined nearer the center of the rotating plasma. Consequently, through this action, the heavier ions are generally separated from the light ions.
Unlike a plasma centrifuge, the present invention pertains to plasma mass filters of the type disclosed in U.S. Pat. No. 6,096,220, which issued to Ohkawa for an invention entitled xe2x80x9cPlasma Mass Filter,xe2x80x9d and which is assigned to the same assignee as the present invention (hereinafter sometimes referred to as the Ohkawa patent). The Ohkawa patent is incorporated herein by reference. In clear contrast with plasma centrifuges, plasma mass filters incorporate crossed electric and magnetic fields (Exc3x97B) that effectively create a potential hill in the chamber of the filter for the heavier ions (M1). Such a potential hill, however, prevents the passage of a charged particle (e.g. a light ion, M2) across the potential hill (barrier) unless it has energy greater than that corresponding to the potential hill (barrier). For a plasma mass filter, the establishment of the potential hill is accomplished by directing the radial electric field, Er, in a direction that is opposite to that of a conventional centrifuge.
As disclosed in the Ohkawa patent, the determination as to whether an ion is a heavy ion (M1) or a light ion (M2), is dependent on its relationship to a so-called cut-off mass (Mc). As defined in the Ohkawa patent, the cut-off mass for ion differentiation is expressed as:
Mc=zea2(Bz)2/8Vctr
wherein xe2x80x9czexe2x80x9d is the ion charge, xe2x80x9caxe2x80x9d is the distance of the plasma chamber wall from its longitudinal axis, wherein the magnetic field has a magnitude xe2x80x9cB2xe2x80x9d in a direction along the longitudinal axis, and there is a positive potential on the longitudinal axis that has a value xe2x80x9cVctrxe2x80x9d, and further wherein the chamber wall has a substantially zero potential. Under these conditions, heavy ions (M1) are defined as having mass to charge ratios greater than the cut-off mass (Mc), with light ions (M2) having mass to charge ratios less than the cut-off mass (Mc), (i.e. M1 greater than Mc greater than M2).
Heretofore, the standard operating procedure for a plasma mass filter has been to establish a plasma throughput, xcex93, such that the plasma density remains below a defined collisional density, nc. More specifically, for the purposes of the present invention, the xe2x80x9ccollisional density,xe2x80x9d nc, is defined as being a plasma density wherein there is a probability of xe2x80x9conexe2x80x9d that an ion collision will occur within a single orbital rotation of an ion around the chamber axis under the influence of crossed electric and magnetic fields (Exc3x97B). In other words, a collisional density, nc, is established when it is just as likely that an ion will collide with another ion, as it is that the ion will not collide with another ion during a single orbital rotation. In order to improve the plasma throughput, xcex93, of a plasma filter, however, it may be desirable to operate the filter with plasma densities above the collisional density, nc. Fortunately, as recognized by the present invention, the effective operation of a plasma mass filter is possible under controlled conditions with plasma densities substantially above the collisional density, if the device is long enough to allow radial collection of collision impeded heavy ions.
In light of the above, it is an object of the present invention to provide a high throughput plasma mass filter which is effective in its operation with plasma densities above a collisional density, nc. Another object of the present invention is to provide a high throughput plasma mass filter which effectively separates ions of relatively high mass to charge ratios, M1, from ions of relatively low mass to charge ratios, M2, when M1 is generally greater than 2M2. Still another object of the present invention is to establish an operating regime for a high throughput plasma mass filter which increases its throughput capability. Yet another object of the present invention is to provide a high throughput plasma mass filter which is relatively easy to manufacture, is simple to use, and is comparatively cost effective.
For the purposes of the present invention, the term xe2x80x9ccollisional densityxe2x80x9d (nc) is defined as being a plasma density wherein there is a probability of xe2x80x9conexe2x80x9d that an ion will experience a collision with another ion during a single orbital rotation of the ion around an axis. Specifically, such a rotation is considered to be around the axis of a plasma mass filter under the influence of crossed electric and magnetic fields (Exc3x97B). Stated differently, a collisional density (nc) is established whenever it is just as likely that an ion will collide with another ion during a single orbital rotation about the filter""s axis, as it is that the ion will not collide with another ion during the rotation. The main premise of the present invention is that a plasma mass filter can be operated to separate heavy ions from light ions, even when plasma densities are substantially greater than the collisional density (nc).
As intended for the present invention, after the heavy and light ions have been separated from each other, the filter""s throughput (xcex93) will be composed almost entirely of light ions (M2) from the plasma. Accordingly, for a single emitted device, this throughput can be mathematically expressed as:
xcex93=xcfx80a2n2vz.xe2x80x83xe2x80x83(eqn. 1)
In this expression, n2 is the density of the light ions per unit volume, and vz is the velocity of the plasma (for both the heavy and light ions) along the longitudinal axis of the plasma mass filter. In contrast to a collisionless filter where the heavy ions are lost very rapidly to the heavy collectors surrounding the injection zone, the heavy ions in the high throughput filter are impeded in their radial motion by collisions with other ions. As a consequence, the equivalent radial velocity of the heavy ions is reduced. Thus, for a given length device, the number of heavy ions reaching the light collector can be estimated by solving a simplified continuity equation:                                                         v              z                        ⁢                          ∂                              ∂                z                                      ⁢            n                    +                                    1              r                        ⁢                          xe2x80x83                        ⁢                          ∂                              ∂                r                                      ⁢                          xe2x80x83                        ⁢                          (                              rnv                r                            )                                      =        0                            (eqn.   2)            
Assuming there is no radial dependence of the density or the heavy ion velocity and no axial variation in the heavy ion axial velocity, the above eqn. 2 gives:
Logxcex8(n(z)/n0)=xe2x88x92(Lvr/rvz)=Fxe2x80x83xe2x80x83(eqn. 3)
where F is the logarithmic separation factor, L is the length of the device, vz is the axial velocity of the heavy ions, vr is the radial velocity of the heavy ions, and r is the distance to the wall from the starting point. It is clear from equation (3) that for good separation, the length has to be long enough to allow the heavy ions to escape radially before they transit the device (F is the ratio of the axial loss time to the radial loss time for the heavy ions). The heavy ion radial velocity can be obtained from the equations of motion including collisions. More particularly, a range for the radial velocity xe2x80x9cvrxe2x80x9d can be determined by considering boundary conditions where: 1) the rotational velocity of the heavy ions, M1, is zero (vxcex8=0); and 2) where this rotational velocity equals that of the light ions, M2 (vxcex8=vxcex8xe2x80x2). With these boundary conditions, the radial velocity, vr, can be mathematically expressed as:
vr=r[xcexa9cxcexa9*/4v]xcex5.xe2x80x83xe2x80x83(eqn. 4)
In the above expression: xe2x80x9cvxe2x80x9d is the ion-ion collision frequency; xe2x80x9cxcexa9cxe2x80x9d is the cyclotron frequency for an ion of cut-off mass, Mc, and xe2x80x9cxcexa9*xe2x80x9d is the cyclotron frequency of the light ions M2. For case 1 above, xcex5=1 and for case 2, xcex5=[M1xe2x88x92M2]/4Mc so xcex5 can be evaluated more precisely in actual cases. An important observation from these relationships is the fact that xe2x80x9cvrxe2x80x9d is a function of xcexa9c, xcexa9*, and xcexd. A high throughput plasma mass filter in accordance with the present invention includes a substantially cylindrical shaped plasma chamber. The chamber has a length xe2x80x9cLxe2x80x9d and defines a longitudinal axis. Further, it has a wall that is located at a radial distance xe2x80x9caxe2x80x9d from the axis. Magnetic coils are mounted on the wall of the chamber to generate a magnetic field (B) in the chamber having a magnitude B. Also, a series of conducting rings are mounted on the chamber and are centered on the longitudinal axis to generate a radial electric field E. A spiral electrode could also be used for this purpose.
Inside the chamber of the plasma mass filter, the magnetic field (B) is oriented substantially parallel to the axis, and the electric field (E) is oriented substantially perpendicular to the magnetic field to cross the electric field with the magnetic field (Exc3x97B). Also, it is an important aspect of the present invention that the electric field has a positive potential (Vctr) on the longitudinal axis and a substantially zero potential on the wall.
In operation, a multi-species plasma is introduced into the chamber with an initial plasma density that is substantially greater than the collisional density. As envisioned by the present invention, this multi-species plasma will include both ions having a relatively high mass to charge ratio (M1) and ions having a relatively low mass to charge ratio (M2). Theoretically, the crossed electric and magnetic fields (Exc3x97B) are configured to remove the heavy ions (M1) in a length, L, and provide a throughput (xcex93) for the light ions (M2) as they transit through the chamber.
In order to mathematically determine how an ion in the multi-species plasma will be affected by the high throughput plasma mass filter, it is necessary to determine whether the charged particle is a heavy ion (M1) or a light ion (M2). For the present invention, this distinction is made relative to a particle having a predetermined cut-off mass (Mc). Specifically, a relationship is established for M1 greater than Mc greater than M2, by the expression below, wherein xe2x80x9cexe2x80x9d is the charge of a singly ionized ion:
Mc=zea2(Bz)2/8Vctr.
The operating parameters of the plasma mass filter for separating heavy ions (M1) from light ions (M2) can be established by first determining a value for E where generally:
[M1xe2x88x92M2]4Mcxe2x89xa6xcex5xe2x89xa61.
When considering xe2x80x9cxcex5xe2x80x9d, and referring back to (eqn. 4), it is to be appreciated that for purposes of the present invention, it is preferable for the heavy ions (M1) to have more than about twice the mass of the light ions (M2), (i.e. M1 greater than 2M2). It is clear that a filter device designed for high throughput requires a longer total length than a standard filter and a proportionally longer heavy ion collector.